{"id":7740,"date":"2022-05-14T10:36:05","date_gmt":"2022-05-14T08:36:05","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7740"},"modified":"2022-05-14T10:36:05","modified_gmt":"2022-05-14T08:36:05","slug":"pfh-la-semana-en-exercitium-del-9-al-13-de-mayo-de-2022","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/pfh-la-semana-en-exercitium-del-9-al-13-de-mayo-de-2022\/","title":{"rendered":"PFH: La semana en Exercitium (del 9 al 13 de mayo de 2022)"},"content":{"rendered":"<p>Esta semana he publicado en <a href=\"http:\/\/bit.ly\/2sqPtGs\">Exercitium<\/a> las soluciones de los siguientes problemas:<\/p>\n<ul>\n<li><a href=\"#ej1\">1. M\u00ednimo producto escalar<\/a><\/li>\n<li><a href=\"#ej2\">2. Particiones de enteros positivos<\/a><\/li>\n<li><a href=\"#ej3\">3. Reconocimiento de potencias de 2<\/a><\/li>\n<li><a href=\"#ej4\">4. Conjunto de divisores<\/a><\/li>\n<li><a href=\"#ej5\">5. N\u00famero de divisores<\/a><\/li>\n<\/ul>\n<p>A continuaci\u00f3n se muestran las soluciones.<br \/>\n<!--more--><br \/>\n<a name=\"ej1\"><\/a><\/p>\n<h3>1. M\u00ednimo producto escalar<\/h3>\n<p>El producto escalar de los vectores [a1,a2,&#8230;,an] y [b1,b2,&#8230;, bn] es<\/p>\n<pre lang=\"text\">\n   a1 * b1 + a2 * b2 + \u00b7\u00b7\u00b7 + an * bn.\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   menorProductoEscalar :: (Ord a, Num a) => [a] -> [a] -> a\n<\/pre>\n<p>tal que <code>(menorProductoEscalar xs ys)<\/code> es el m\u00ednimo de los productos<br \/>\nescalares de las permutaciones de <code>xs<\/code> y de las permutaciones de<br \/>\n<code>ys<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   menorProductoEscalar [3,2,5]  [1,4,6]    == 29\n   menorProductoEscalar [3,2,5]  [1,4,-6]   == -19\n   menorProductoEscalar [1..10^2] [1..10^2] == 171700\n   menorProductoEscalar [1..10^3] [1..10^3] == 167167000\n   menorProductoEscalar [1..10^4] [1..10^4] == 166716670000\n   menorProductoEscalar [1..10^5] [1..10^5] == 166671666700000\n   menorProductoEscalar [1..10^6] [1..10^6] == 166667166667000000\n<\/pre>\n<p><!--more--><\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nmodule Minimo_producto_escalar where\n\nimport Data.List (sort, permutations)\nimport Test.QuickCheck (quickCheck)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nmenorProductoEscalar1 :: (Ord a, Num a) => [a] -> [a] -> a\nmenorProductoEscalar1 xs ys =\n  minimum [sum (zipWith (*) pxs pys) | pxs <- permutations xs,\n                                       pys <- permutations ys]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nmenorProductoEscalar2 :: (Ord a, Num a) => [a] -> [a] -> a\nmenorProductoEscalar2 xs ys =\n  minimum [sum (zipWith (*) pxs ys) | pxs <- permutations xs]\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nmenorProductoEscalar3 :: (Ord a, Num a) => [a] -> [a] -> a\nmenorProductoEscalar3 xs ys =\n  sum (zipWith (*) (sort xs) (reverse (sort ys)))\n\n-- Equivalencia\n-- ============\n\n-- La propiedad es\nprop_menorProductoEscalar :: [Integer] -> [Integer] -> Bool\nprop_menorProductoEscalar xs ys =\n  all (== menorProductoEscalar1 xs' ys')\n      [menorProductoEscalar2 xs' ys',\n       menorProductoEscalar3 xs' ys']\n  where n   = min (length xs) (length ys)\n        xs' = take n xs\n        ys' = take n ys\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheckWith (stdArgs {maxSize=7}) prop_menorProductoEscalar\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> menorProductoEscalar1 [0..5] [0..5]\n--    20\n--    (3.24 secs, 977385528 bytes)\n--    \u03bb> menorProductoEscalar2 [0..5] [0..5]\n--    20\n--    (0.01 secs, 4185776 bytes)\n--\n--    \u03bb> menorProductoEscalar2 [0..9] [0..9]\n--    120\n--    (23.86 secs, 9342872784 bytes)\n--    \u03bb> menorProductoEscalar3 [0..9] [0..9]\n--    120\n--    (0.01 secs, 2580824 bytes)\n--\n--    \u03bb> menorProductoEscalar3 [0..10^6] [0..10^6]\n--    166666666666500000\n--    (2.46 secs, 473,338,912 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Minimo_producto_escalar.hs\">GitHub<\/a>.<\/p>\n<p><a name=\"ej2\"><\/a><\/p>\n<h3>2. Particiones de enteros positivos<\/h3>\n<p>Una partici\u00f3n de un entero positivo n es una manera de escribir n como una suma de enteros positivos. Dos sumas que s\u00f3lo difieren en el orden de sus sumandos se consideran la misma partici\u00f3n. Por ejemplo, 4 tiene cinco particiones: 4, 3+1, 2+2, 2+1+1 y 1+1+1+1.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   particiones :: Int -> [[Int]]\n<\/pre>\n<p>tal que <code>(particiones n)<\/code> es la lista de las particiones del n\u00famero <code>n<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   particiones 4  ==  [[4],[3,1],[2,2],[2,1,1],[1,1,1,1]]\n   particiones 5  ==  [[5],[4,1],[3,2],[3,1,1],[2,2,1],[2,1,1,1],[1,1,1,1,1]]\n   length (particiones 50)  ==  204226\n<\/pre>\n<p><!--more--><\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nmodule Particiones_de_enteros_positivos where\n\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nparticiones1 :: Int -> [[Int]]\nparticiones1 0 = [[]]\nparticiones1 n = [x:y | x <- [n,n-1..1],\n                        y <- particiones1 (n-x),\n                        [x] >= take 1 y]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nparticiones2 :: Int -> [[Int]]\nparticiones2 n = aux !! n\n  where\n    aux = [] : map particiones [1..]\n    particiones m = [m] : [x:p | x <- [m,m-1..1],\n                                 p <- aux !! (m-x),\n                                 x >= head p]\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nparticiones3 :: Int -> [[Int]]\nparticiones3 n = aux n n\n  where aux 0 _ = [[]]\n        aux n' m = concat [map (i:) (aux (n'-i) i)\n                          | i <- [n',n'-1..1], i <= m]\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nparticiones4 :: Int -> [[Int]]\nparticiones4 n = aux n n\n  where aux 0 _ = [[]]\n        aux n' m = concat [map (i:) (aux (n'-i) i)\n                          | i <- [k,k-1..1]]\n          where k = min m n'\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_particiones :: Positive Int -> Bool\nprop_particiones (Positive n) =\n  all (== particiones1 n)\n      [ particiones2 n\n      , particiones3 n\n      , particiones4 n\n      ]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheckWith (stdArgs {maxSize=20}) prop_particiones\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia                                        --\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> length (particiones1 23)\n--    1255\n--    (12.50 secs, 6,614,487,992 bytes)\n--    \u03bb> length (particiones2 23)\n--    1255\n--    (0.04 secs, 3,071,104 bytes)\n--    \u03bb> length (particiones3 23)\n--    1255\n--    (0.02 secs, 9,163,544 bytes)\n--    \u03bb> length (particiones4 23)\n--    1255\n--    (0.01 secs, 7,149,512 bytes)\n--\n--    \u03bb> length (particiones2 50)\n--    204226\n--    (2.50 secs, 758,729,104 bytes)\n--    \u03bb> length (particiones3 50)\n--    204226\n--    (4.26 secs, 2,359,121,096 bytes)\n--    \u03bb> length (particiones4 50)\n--    204226\n--    (2.67 secs, 1,598,588,040 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Particiones_de_enteros_positivos.hs\">GitHub<\/a>.<\/p>\n<p><a name=\"ej3\"><\/a><\/p>\n<h3>3. Reconocimiento de potencias de 2<\/h3>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   esPotenciaDeDos :: Integer -> Bool\n<\/pre>\n<p>tal que <code>(esPotenciaDeDos n)<\/code> se verifica si <code>n<\/code> es una potencia de dos (suponiendo que <code>n<\/code> es mayor que 0). Por ejemplo.<\/p>\n<pre lang=\"text\">\n   esPotenciaDeDos    1        == True\n   esPotenciaDeDos    2        == True\n   esPotenciaDeDos    6        == False\n   esPotenciaDeDos    8        == True\n   esPotenciaDeDos 1024        == True\n   esPotenciaDeDos 1026        == False\n   esPotenciaDeDos (2^(10^8))  == True\n<\/pre>\n<p><!--more--><\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Bits ((.&.))\nimport Data.Numbers.Primes (primeFactors)\nimport Test.QuickCheck (Positive (Positive), quickCheck)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nesPotenciaDeDos1 :: Integer -> Bool\nesPotenciaDeDos1 1 = True\nesPotenciaDeDos1 n\n  | even n    = esPotenciaDeDos1 (n `div` 2)\n  | otherwise = False\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nesPotenciaDeDos2 :: Integer -> Bool\nesPotenciaDeDos2 n = n ==\n  head (dropWhile (<n) potenciasDeDos)\n\n-- potenciasDeDos es la lista de las potencias de dos. Por ejemplo,\n--    take 10 potenciasDeDos  == [1,2,4,8,16,32,64,128,256,512]\npotenciasDeDos :: [Integer]\npotenciasDeDos = iterate (*2) 1\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nesPotenciaDeDos3 :: Integer -> Bool\nesPotenciaDeDos3 x = all (==2) (primeFactors x)\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\n-- Usando la funci\u00f3n (.&.) de la librer\u00eda Data.Bits. Dicha funci\u00f3n\n-- calcula el n\u00famero correspondiente a la conjunci\u00f3n de las\n-- representaciones binarias de sus argumentos. Por ejemplo,\n--    6 .&. 3 == 2\n-- ya que\n--    la representaci\u00f3n binaria de 6 es     [1,1,0]\n--    la representaci\u00f3n binaria de 3 es       [1,1]\n--    la conjunci\u00f3n es                        [1,0]\n--    la representaci\u00f3n decimal de [1,0] es   2\n--\n-- Otros ejemplos:\n--    4 .&. 3 ==   [1,0,0] .&.   [1,1] == 0\n--    8 .&. 7 == [1,0,0,0] .&. [1,1,1] = 0\n\nesPotenciaDeDos4 :: Integer -> Bool\nesPotenciaDeDos4 n = n .&. (n-1) == 0\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_esPotenciaDeDos :: Positive Integer -> Bool\nprop_esPotenciaDeDos (Positive n) =\n  all (== esPotenciaDeDos1 n)\n      [ esPotenciaDeDos2 n\n      , esPotenciaDeDos3 n\n      , esPotenciaDeDos4 n\n      ]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_esPotenciaDeDos\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> esPotenciaDeDos1 (2^(3*10^5))\n--    True\n--    (3.51 secs, 5,730,072,544 bytes)\n--    \u03bb> esPotenciaDeDos2 (2^(3*10^5))\n--    True\n--    (3.12 secs, 5,755,639,952 bytes)\n--    \u03bb> esPotenciaDeDos3 (2^(3*10^5))\n--    True\n--    (2.92 secs, 5,758,872,040 bytes)\n--    \u03bb> esPotenciaDeDos4 (2^(3*10^5))\n--    True\n--    (0.03 secs, 715,152 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Reconocimiento_de_grandes_potencias_de_2.hs\">GitHub<\/a>.<\/p>\n<p><a name=\"ej4\"><\/a><\/p>\n<h3>4. Conjunto de divisores<\/h3>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   divisores :: Integer -> [Integer]\n<\/pre>\n<p>tal que <code>(divisores x)<\/code> es el conjunto de divisores de <code>x<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n  divisores 30  ==  [1,2,3,5,6,10,15,30]\n  length (divisores (product [1..10]))  ==  270\n  length (divisores (product [1..25]))  ==  340032\n<\/pre>\n<p><!--more--><\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (group, inits, nub, sort, subsequences)\nimport Data.Numbers.Primes (primeFactors)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\ndivisores1 :: Integer -> [Integer]\ndivisores1 n = [x | x <- [1..n], n `rem` x == 0]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\ndivisores2 :: Integer -> [Integer]\ndivisores2 n = filter ((== 0) . mod n) [1..n]\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\ndivisores3 :: Integer -> [Integer]\ndivisores3 =\n  nub . sort . map product . subsequences . primeFactors\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\ndivisores4 :: Integer -> [Integer]\ndivisores4 =\n  sort\n  . map (product . concat)\n  . productoCartesiano\n  . map inits\n  . group\n  . primeFactors\n\n-- (productoCartesiano xss) es el producto cartesiano de los conjuntos\n-- xss. Por ejemplo,\n--    \u03bb> productoCartesiano [[1,3],[2,5],[6,4]]\n--    [[1,2,6],[1,2,4],[1,5,6],[1,5,4],[3,2,6],[3,2,4],[3,5,6],[3,5,4]]\nproductoCartesiano :: [[a]] -> [[a]]\nproductoCartesiano []       = [[]]\nproductoCartesiano (xs:xss) =\n  [x:ys | x <- xs, ys <- productoCartesiano xss]\n\n-- 5\u00aa soluci\u00f3n\n-- ===========\n\ndivisores5 :: Integer -> [Integer]\ndivisores5 = sort\n           . map (product . concat)\n           . sequence\n           . map inits\n           . group\n           . primeFactors\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_divisores :: Positive Integer -> Bool\nprop_divisores (Positive n) =\n  all (== divisores1 n)\n      [ divisores2 n\n      , divisores3 n\n      , divisores4 n\n      , divisores5 n\n      ]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_divisores\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de la eficiencia\n-- ============================\n\n--    \u03bb> length (divisores (product [1..11]))\n--    540\n--    (12.51 secs, 7,983,499,736 bytes)\n--    \u03bb> length (divisores2 (product [1..11]))\n--    540\n--    (4.81 secs, 4,790,146,656 bytes)\n--    \u03bb> length (divisores3 (product [1..11]))\n--    540\n--    (0.10 secs, 107,339,848 bytes)\n--    \u03bb> length (divisores4 (product [1..11]))\n--    540\n--    (0.02 secs, 1,702,616 bytes)\n--    \u03bb> length (divisores5 (product [1..11]))\n--    540\n--    (0.02 secs, 1,205,824 bytes)\n--\n--    \u03bb> length (divisores3 (product [1..14]))\n--    2592\n--    (7.89 secs, 9,378,454,912 bytes)\n--    \u03bb> length (divisores4 (product [1..14]))\n--    2592\n--    (0.03 secs, 9,426,528 bytes)\n--    \u03bb> length (divisores5 (product [1..14]))\n--    2592\n--    (0.02 secs, 6,636,608 bytes)\n--\n--    \u03bb> length (divisores4 (product [1..25]))\n--    340032\n--    (1.65 secs, 2,055,558,208 bytes)\n--    \u03bb> length (divisores5 (product [1..25]))\n--    340032\n--    (0.88 secs, 1,532,515,304 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Conjunto_de_divisores.hs\">GitHub<\/a>.<\/p>\n<p><a name=\"ej5\"><\/a><\/p>\n<h3>5. N\u00famero de divisores<\/h3>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   numeroDivisores :: Integer -> Integer\n<\/pre>\n<p>tal que <code>(numeroDivisores x)<\/code> es el n\u00famero de divisores de <code>x<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   numeroDivisores 12  ==  6\n   numeroDivisores 25  ==  3\n   length (show (numeroDivisores (product [1..3*10^4])))  ==  1948\n<\/pre>\n<p><!--more--><\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (genericLength, group, inits)\nimport Data.Numbers.Primes (primeFactors)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nnumeroDivisores1 :: Integer -> Integer\nnumeroDivisores1 x =\n  genericLength [y | y <- [1..x], x `mod` y == 0]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nnumeroDivisores2 :: Integer -> Integer\nnumeroDivisores2 1 = 1\nnumeroDivisores2 x\n  | esCuadrado x = 2 * genericLength [y | y <- [1..raizEntera x], x `mod` y == 0] - 1\n  | otherwise    = 2 * genericLength [y | y <- [1..raizEntera x], x `mod` y == 0]\n\n-- (raizEntera x) es el mayor n\u00famero entero cuyo cuadrado es menor o\n-- igual que x. Por ejemplo,\n--    raizEntera 3  ==  1\n--    raizEntera 4  ==  2\n--    raizEntera 5  ==  2\n--    raizEntera 8  ==  2\n--    raizEntera 9  ==  3\nraizEntera :: Integer -> Integer\nraizEntera x = floor (sqrt (fromInteger x))\n\n-- (esCuadrado x) se verifica si x es un cuadrado perfecto. Por ejemplo,\n--    esCuadrado 9  ==  True\n--    esCuadrado 7  ==  False\nesCuadrado :: Integer -> Bool\nesCuadrado x =\n  x == (raizEntera x)^2\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nnumeroDivisores3 :: Integer -> Integer\nnumeroDivisores3 =\n  genericLength . divisores\n\n-- (divisores x) es la lista de los divisores de x. Por ejemplo,\n--    divisores 12  ==  [1,3,2,6,4,12]\n--    divisores 25  ==  [1,5,25]\ndivisores :: Integer -> [Integer]\ndivisores = map (product . concat)\n          . productoCartesiano\n          . map inits\n          . group\n          . primeFactors\n\n-- (productoCartesiano xss) es el producto cartesiano de los conjuntos\n-- xss. Por ejemplo,\n--    \u03bb> productoCartesiano [[1,3],[2,5],[6,4]]\n--    [[1,2,6],[1,2,4],[1,5,6],[1,5,4],[3,2,6],[3,2,4],[3,5,6],[3,5,4]]\nproductoCartesiano :: [[a]] -> [[a]]\nproductoCartesiano []       = [[]]\nproductoCartesiano (xs:xss) =\n  [x:ys | x <- xs, ys <- productoCartesiano xss]\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nnumeroDivisores4 :: Integer -> Integer\nnumeroDivisores4 = genericLength\n                 . map (product . concat)\n                 . sequence\n                 . map inits\n                 . group\n                 . primeFactors\n\n-- 5\u00aa soluci\u00f3n\n-- ===========\n\nnumeroDivisores5 :: Integer -> Integer\nnumeroDivisores5 =\n  product . map ((+1) . genericLength) . group . primeFactors\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_numeroDivisores :: Positive Integer -> Bool\nprop_numeroDivisores (Positive x) =\n  all (== numeroDivisores1 x)\n      [ numeroDivisores2 x\n      , numeroDivisores3 x\n      , numeroDivisores4 x\n      , numeroDivisores5 x]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_numeroDivisores\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> numeroDivisores1 (product [1..10])\n--    270\n--    (1.67 secs, 726,327,208 bytes)\n--    \u03bb> numeroDivisores2 (product [1..10])\n--    270\n--    (0.01 secs, 929,000 bytes)\n--\n--    \u03bb> numeroDivisores2 (product [1..16])\n--    5376\n--    (2.10 secs, 915,864,664 bytes)\n--    \u03bb> numeroDivisores3 (product [1..16])\n--    5376\n--    (0.01 secs, 548,472 bytes)\n--\n--    \u03bb> numeroDivisores3 (product [1..30])\n--    2332800\n--    (3.80 secs, 4,149,811,688 bytes)\n--    \u03bb> numeroDivisores4 (product [1..30])\n--    2332800\n--    (0.59 secs, 722,253,848 bytes)\n--    \u03bb> numeroDivisores5 (product [1..30])\n--    2332800\n--    (0.00 secs, 587,856 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Numero_de_divisores.hs\">GitHub<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Esta semana he publicado en Exercitium las soluciones de los siguientes problemas: 1. M\u00ednimo producto escalar 2. Particiones de enteros positivos 3. Reconocimiento de potencias de 2 4. Conjunto de divisores 5. N\u00famero de divisores A continuaci\u00f3n se muestran las soluciones.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[337],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":false,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7740"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/comments?post=7740"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7740\/revisions"}],"predecessor-version":[{"id":7741,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7740\/revisions\/7741"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7740"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7740"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7740"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}